%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL712^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:32 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 143 ( 51 unt; 0 typ; 12 def)
% Number of atoms : 982 ( 225 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1376 ( 152 ~; 252 |; 17 &; 845 @)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 204 ( 204 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 18 con; 0-4 aty)
% ( 82 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 375 ( 0 sgn 128 !; 1 ?; 375 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_54,type,
sK7: $i > $o ).
thf(func_def_57,type,
sK10: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( mtransitive @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( mtransitive @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f36,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f37,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f40,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( mtransitive @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
=> ( ( mtransitive @ X0 )
= $true ) ),
inference(fool_elimination,[],[f44]) ).
thf(f54,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f70,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f71,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f82,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f83,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
& ( ( mtransitive @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f45]) ).
thf(f88,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) ) ) )
= $true )
& ( ( mtransitive @ sK0 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f90,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f91,plain,
( ( mtransitive @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f92,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f93,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f103,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f114,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f121,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f103,f121,f100]) ).
thf(f133,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f92,f97,f90,f125,f93,f93,f93]) ).
thf(f134,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f91,f114]) ).
thf(f135,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f135]) ).
thf(f137,plain,
$true = sF1,
inference(definition_folding,[],[f133,f136]) ).
thf(f138,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f139,plain,
sF2 != $true,
inference(definition_folding,[],[f134,f138]) ).
thf(f140,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f138]) ).
thf(f151,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f152,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK5 )
= $false )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( sF2 = $true )
| ( ( ( ( sK0 @ sK5 @ sK4 )
& ( sK0 @ sK4 @ sK3 ) )
=> ( sK0 @ sK5 @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( sF2 = $true )
| ( $false
= ( sK0 @ sK5 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( ( sK0 @ sK5 @ sK4 )
& ( sK0 @ sK4 @ sK3 ) )
= $true )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( sF2 = $true )
| ( $true
= ( sK0 @ sK4 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( sF2 = $true )
| ( ( sK0 @ sK5 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
| ( sF1 = $false ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f186,plain,
( ( sF1 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( sF1 = $false )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) )
= $true )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( sF1 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) ) )
| ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= $false )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( sF1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK10 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( sK0 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( sF1 = $false )
| ( ( ~ ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) )
| ( X2 @ ( sK10 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( sF1 = $false )
| ( ( ~ ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) )
| ( X2 @ ( sK10 @ X1 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) )
= $true )
| ( sF1 = $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( ( ~ ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( ( ~ ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
= $false )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ~ ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
= $false )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( ~ ( sK0 @ X3 @ X4 )
| ( X2 @ X4 ) )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( sK0 @ X3 @ X4 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X4 ) )
| ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f206,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( sF1 = $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( ( ~ ( sK0 @ X3 @ X4 )
| ( X2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $true
= ( X2 @ X4 ) )
| ( $true
= ( ~ ( sK0 @ X3 @ X4 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( X2 @ X4 ) )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f219,definition,
( spl11_3
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f223,definition,
( spl11_4
<=> ( ( sK0 @ sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f225,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $true )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f161,f223,f219]) ).
thf(f228,definition,
( spl11_5
<=> ( $true
= ( sK0 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f230,plain,
( ( $true
= ( sK0 @ sK4 @ sK3 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl11_3
| spl11_5 ),
inference(avatar_split_clause,[],[f160,f228,f219]) ).
thf(f233,definition,
( spl11_6
<=> ( $false
= ( sK0 @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f235,plain,
( ( $false
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,plain,
( spl11_3
| spl11_6 ),
inference(avatar_split_clause,[],[f158,f233,f219]) ).
thf(f241,definition,
( spl11_8
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f243,plain,
( ( $true = sF1 )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f261,definition,
( spl11_12
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f262,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X4 ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,definition,
( spl11_13
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f266,plain,
( ( sF1 = $false )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( spl11_12
| spl11_13 ),
inference(avatar_split_clause,[],[f204,f264,f261]) ).
thf(f269,definition,
( spl11_14
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X4 ) )
| ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f270,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK10 @ X1 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( X2 @ X4 ) )
| ( ( sK0 @ X3 @ X4 )
= $false ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl11_13
| spl11_14 ),
inference(avatar_split_clause,[],[f209,f269,f264]) ).
thf(f272,plain,
spl11_8,
inference(avatar_split_clause,[],[f137,f241]) ).
thf(f273,plain,
~ spl11_3,
inference(avatar_split_clause,[],[f139,f219]) ).
thf(f274,plain,
( ( $true = $false )
| ~ spl11_8
| ~ spl11_13 ),
inference(forward_demodulation,[],[f266,f243]) ).
thf(f275,plain,
( $false
| ~ spl11_8
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f276,plain,
( ~ spl11_8
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f275]) ).
thf(f323,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK0 @ X0 @ X4 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) )
| ( $true = $false )
| ( ( sK0 @ X0 @ X3 )
= $false )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl11_12
| ~ spl11_14 ),
inference(constrained_superposition,[],[f270,f262]) ).
thf(f327,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X0 @ X4 ) )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X0 @ X3 )
= $false ) )
| ~ spl11_12
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f332,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ sK5 @ X2 )
= $false )
| ( $true = $false )
| ( $true
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ sK5 @ X0 )
= $false ) )
| ~ spl11_6
| ~ spl11_12
| ~ spl11_14 ),
inference(constrained_superposition,[],[f235,f327]) ).
thf(f343,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( ( sK0 @ sK5 @ X0 )
= $false )
| ( ( sK0 @ sK5 @ X2 )
= $false )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( $true
= ( sK0 @ sK5 @ X1 ) ) )
| ~ spl11_6
| ~ spl11_12
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f345,definition,
( spl11_15
<=> ! [X2: $i] :
( ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( ( sK0 @ sK5 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f346,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( ( sK0 @ sK5 @ X2 )
= $false ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f348,definition,
( spl11_16
<=> ! [X0: $i,X1: $i] :
( ( ( sK0 @ sK5 @ X0 )
= $false )
| ( $true
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f349,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ sK5 @ X0 )
= $false ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f351,plain,
( spl11_16
| spl11_15
| ~ spl11_6
| ~ spl11_12
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f343,f269,f261,f233,f345,f348]) ).
thf(f352,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl11_5
| ~ spl11_15 ),
inference(constrained_superposition,[],[f346,f230]) ).
thf(f360,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ~ spl11_5
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f365,plain,
( ( $true = $false )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_15 ),
inference(forward_demodulation,[],[f360,f225]) ).
thf(f366,plain,
( $false
| ~ spl11_4
| ~ spl11_5
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f367,plain,
( ~ spl11_4
| ~ spl11_5
| ~ spl11_15 ),
inference(avatar_contradiction_clause,[],[f366]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $true = $false )
| ( ( sK0 @ sK5 @ X0 )
= $false ) )
| ~ spl11_6
| ~ spl11_16 ),
inference(constrained_superposition,[],[f349,f235]) ).
thf(f374,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ sK5 @ X0 )
= $false ) )
| ~ spl11_6
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f378,plain,
( spl11_15
| ~ spl11_6
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f374,f348,f233,f345]) ).
cnf(s2,plain,
( spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s3,plain,
( spl11_3
| spl11_5 ),
inference(sat_conversion,[],[f231]) ).
cnf(s4,plain,
( spl11_3
| spl11_6 ),
inference(sat_conversion,[],[f236]) ).
cnf(s9,plain,
( spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f267]) ).
cnf(s10,plain,
( spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f271]) ).
cnf(s11,plain,
spl11_8,
inference(sat_conversion,[],[f272]) ).
cnf(s12,plain,
~ spl11_3,
inference(sat_conversion,[],[f273]) ).
cnf(s13,plain,
( ~ spl11_8
| ~ spl11_13 ),
inference(sat_conversion,[],[f276]) ).
cnf(s18,plain,
( ~ spl11_6
| ~ spl11_12
| ~ spl11_14
| spl11_15
| spl11_16 ),
inference(sat_conversion,[],[f351]) ).
cnf(s20,plain,
( ~ spl11_4
| ~ spl11_5
| ~ spl11_15 ),
inference(sat_conversion,[],[f367]) ).
cnf(s21,plain,
( ~ spl11_6
| spl11_15
| ~ spl11_16 ),
inference(sat_conversion,[],[f378]) ).
cnf(s24,plain,
~ spl11_13,
inference(rat,[],[s13,s11]) ).
cnf(s25,plain,
spl11_14,
inference(rat,[],[s10,s24]) ).
cnf(s26,plain,
spl11_12,
inference(rat,[],[s9,s24]) ).
cnf(s27,plain,
spl11_6,
inference(rat,[],[s4,s12]) ).
cnf(s28,plain,
spl11_5,
inference(rat,[],[s3,s12]) ).
cnf(s29,plain,
spl11_4,
inference(rat,[],[s2,s12]) ).
cnf(s30,plain,
~ spl11_15,
inference(rat,[],[s20,s28,s29]) ).
cnf(s32,plain,
~ spl11_16,
inference(rat,[],[s21,s27,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s18,s27,s26,s25,s32,s30]) ).
thf(f379,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL712^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n019.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:29:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.35 % (585049)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (585057)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1035109614:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.35 % (585058)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=761608491:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (585055)lrs+10_16_si=on:nwc=1.5:random_seed=3206716585:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (585054)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1414015846:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (585056)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2143058810:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (585056)Instruction limit reached!
% 0.22/0.35 % (585056)------------------------------
% 0.22/0.35 % (585056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585056)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585056)Termination reason: Instruction limit
% 0.22/0.35 % (585056)Termination phase: Saturation
% 0.22/0.35 % (585056)Time elapsed: 0.004 s
% 0.22/0.35 % (585056)Peak memory usage: 11 MB
% 0.22/0.35 % (585056)Instructions burned: 7 (million)
% 0.22/0.35 % (585055)Instruction limit reached!
% 0.22/0.35 % (585055)------------------------------
% 0.22/0.35 % (585055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585055)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585055)Termination reason: Instruction limit
% 0.22/0.35 % (585055)Termination phase: Saturation
% 0.22/0.35 % (585055)Time elapsed: 0.010 s
% 0.22/0.35 % (585055)Peak memory usage: 12 MB
% 0.22/0.35 % (585055)Instructions burned: 19 (million)
% 0.22/0.35 % (585060)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (585060)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.35 % (585059)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=484111478:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (585058)Instruction limit reached!
% 0.22/0.35 % (585058)------------------------------
% 0.22/0.35 % (585058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585058)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585058)Termination reason: Instruction limit
% 0.22/0.35 % (585058)Termination phase: Saturation
% 0.22/0.35 % (585058)Time elapsed: 0.014 s
% 0.22/0.35 % (585058)Peak memory usage: 12 MB
% 0.22/0.35 % (585058)Instructions burned: 25 (million)
% 0.22/0.35 % (585060)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=977275103:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (585066)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4037508207:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (585069)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (585066)Instruction limit reached!
% 0.22/0.35 % (585066)------------------------------
% 0.22/0.35 % (585066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585066)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585066)Termination reason: Instruction limit
% 0.22/0.35 % (585066)Termination phase: Saturation
% 0.22/0.35 % (585066)Time elapsed: 0.003 s
% 0.22/0.35 % (585066)Peak memory usage: 10 MB
% 0.22/0.35 % (585066)Instructions burned: 7 (million)
% 0.22/0.35 % (585067)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4205963908:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.35 % (585069)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=237109319:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.35 % (585067)Instruction limit reached!
% 0.22/0.35 % (585067)------------------------------
% 0.22/0.35 % (585067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585067)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585067)Termination reason: Instruction limit
% 0.22/0.35 % (585067)Termination phase: Property scanning
% 0.22/0.35 % (585067)Time elapsed: 0.003 s
% 0.22/0.35 % (585067)Peak memory usage: 10 MB
% 0.22/0.35 % (585067)Instructions burned: 7 (million)
% 0.22/0.35 % (585060) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-585049-585060"...
% 0.22/0.35 % (585069)Instruction limit reached!
% 0.22/0.35 % (585069)------------------------------
% 0.22/0.35 % (585069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585069)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585069)Termination reason: Instruction limit
% 0.22/0.35 % (585069)Termination phase: Saturation
% 0.22/0.35 % (585069)Time elapsed: 0.003 s
% 0.22/0.35 % (585069)Peak memory usage: 11 MB
% 0.22/0.35 % (585069)Instructions burned: 7 (million)
% 0.22/0.35 % (585060)...printing done.
% 0.22/0.35 % (585060)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.35 % (585060)------------------------------
% 0.22/0.35 % (585060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (585060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (585060)CaDiCaL version: 2.1.3
% 0.22/0.35 % (585060)Termination reason: Refutation
% 0.22/0.35 % (585060)Time elapsed: 0.026 s
% 0.22/0.35 % (585060)Peak memory usage: 13 MB
% 0.22/0.35 % (585060)Instructions burned: 27 (million)
% 0.22/0.35 % (585049)Success in time 0.086 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------